# Fraction Algebra

• Jun 1st 2010, 10:10 PM
Tren301
Fraction Algebra
When 4 is subtracted from the numerator of a fraction, the value of the fraction becomes 2.

When 5 is added to the denominator of the fraction, the value becomes 3/2. Find the fraction.

My guess here is to undo the fraction by multiplying it..............(Thinking)
• Jun 1st 2010, 10:19 PM
Prove It
Quote:

Originally Posted by Tren301
When 4 is subtracted from the numerator of a fraction, the value of the fraction becomes 2.

When 5 is added to the denominator of the fraction, the value becomes 3/2. Find the fraction.

My guess here is to undo the fraction by multiplying it..............(Thinking)

Call the fraction $\displaystyle \frac{x}{y}$.

You're told that when 4 is subtracted from the numerator, the fraction is 2.

So $\displaystyle \frac{x - 4}{y} = 2$

$\displaystyle x - 4 = 2y$

and when 5 is added to the denominator, the fracton is $\displaystyle \frac{3}{2}$.

So $\displaystyle \frac{x}{y + 5} = \frac{3}{2}$

$\displaystyle 2x = 3(y + 5)$

$\displaystyle 2x = 3y + 15$.

So now you have two linear equations

$\displaystyle x - 4 = 2y$

$\displaystyle 2x = 3y + 15$.

Solve them simultaneously, and then you can write what the fraction is.
• Jun 1st 2010, 10:19 PM
Hello Tren301
Quote:

Originally Posted by Tren301
When 4 is subtracted from the numerator of a fraction, the value of the fraction becomes 2.

When 5 is added to the denominator of the fraction, the value becomes 3/2. Find the fraction.

My guess here is to undo the fraction by multiplying it..............(Thinking)

Let the fraction be $\displaystyle \frac ab$, and set up two simultaneous equations:
$\displaystyle \frac{a-4}{b}=2$
and
$\displaystyle \frac{a}{b+5}=\frac32$
Can you continue from here?

PS Ah, I see Prove It has just pipped me to the post!
• Jun 1st 2010, 10:20 PM
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Quote:

Originally Posted by Tren301
When 4 is subtracted from the numerator of a fraction, the value of the fraction becomes 2.

When 5 is added to the denominator of the fraction, the value becomes 3/2. Find the fraction.

My guess here is to undo the fraction by multiplying it..............(Thinking)

Hi Tren301,

This word problem can be translated into equations.

$\displaystyle \frac{p-4}{q}=2$

$\displaystyle \frac{p}{q+5}=\frac{3}{2}$

Can you solve the system?

Edit: Ah we all posted at roughly the same time, but mine came out last.